Results 11 to 20 of about 297 (183)
Ann Comb, 2022 AbstractIn this paper, we expand on the notion of combinatorial presheaf, first introduced explicitly by Aguiar and Mahajan in 2010 but already present in the literature in some other points of view. We do this by adapting the algebraic framework of species to the study of substructures in combinatorics. Afterwards, we consider functions that count the
Penaguiao R.
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Centrification of algebras and Hopf algebras [PDF]
Canadian Mathematical Bulletin, 2021 AbstractWe investigate a method of construction of central deformations of associative algebras, which we call centrification. We prove some general results in the case of Hopf algebras and provide several examples.
Rumynin, Dmitriy, Westaway, Matthew
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Cofree Hopf algebras on Hopf bimodule algebras [PDF]
Journal of Pure and Applied Algebra, 2015 We investigate a Hopf algebra structure on the cotensor coalgebra associated to a Hopf bimodule algebra which contains universal version of Clifford algebras and quantum groups as examples. It is shown to be the bosonization of the quantum quasi-shuffle algebra built on the space of its right coinvariants.
Fang, Xin, Jian, Run-Qiang
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Baxter algebras and Hopf algebras [PDF]
Transactions of the American Mathematical Society, 2003 By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study conditions under which these Hopf algebras are isomorphic.
Andrews, George E. +3 more
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Higher Structures, 2021 We introduce the notion of an oplax Hopf monoid in any braided monoidal bicategory, generalizing that of a Hopf monoid in a braided monoidal category in an appropriate way. We show that Hopf V-categories introduced in [BCV16] are a particular type of oplax Hopf monoids in the monoidal bicategory Span|V described in [Böh17].
Buckley, Mitchell +3 more
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Plethystic Hopf algebras. [PDF]
Proc Natl Acad Sci U S A, 1994 The notion of a plethystic algebra associated with a Hopf algebra endowed with a suitable bilinear form is defined. A special case is the Hopf algebra of symmetric functions.
Rota GC, Stein JA.
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Interacting Hopf algebras [PDF]
Journal of Pure and Applied Algebra, 2017 We introduce the theory IH of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IH are derived using Lack's approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four different monoid-comonoid pairs.
Bonchi F., Sobocinski P., Zanasi F.
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Structure Theorems for Bicomodule Algebras Over Quasi-Hopf Algebras, Weak Hopf Algebras, and Braided Hopf Algebras [PDF]
Communications in Algebra, 2016 24 pages, many ...
Dello, Jeroen +3 more
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Quasisymmetric functions from combinatorial Hopf monoids and Ehrhart Theory [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We investigate quasisymmetric functions coming from combinatorial Hopf monoids. We show that these invariants arise naturally in Ehrhart theory, and that some of their specializations are Hilbert functions for relative simplicial complexes. This class of
Jacob White
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